Answer:
0.6170
Step-by-step explanation:
Given that a manufacturing process is designed to produce bolts with a 0.25-in. diameter.
i.e. no of bolts which are produced as per standard is X means then
X is normal with mean = 0.250 and std dev = 0.04
No of bolts tested = 36
If this mean falls outside the interval (0.230,0.270) the production would be shut down.
i.e. P(|x-25|>0.20) =production shut down probability
![P(|x-25|>0.20)\\=P(|Z|>0.5)\\=2(0.5-0.1915)\\= 0.6170](https://tex.z-dn.net/?f=P%28%7Cx-25%7C%3E0.20%29%5C%5C%3DP%28%7CZ%7C%3E0.5%29%5C%5C%3D2%280.5-0.1915%29%5C%5C%3D%200.6170)
Answer:
![\displaystyle \frac{d}{dx}[3x + 5x] = 8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5B3x%20%2B%205x%5D%20%3D%208)
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: ![\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bcf%28x%29%5D%20%3D%20c%20%5Ccdot%20f%27%28x%29)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
![\displaystyle y = 3x + 5x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%203x%20%2B%205x)
<u>Step 2: Differentiate</u>
- Simplify:
![\displaystyle y = 8x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%208x)
- Derivative Property [Multiplied Constant]:
![\displaystyle y' = 8\frac{d}{dx}[x]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%208%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5D)
- Basic Power Rule:
![\displaystyle y' = 8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%208)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
431.2+826.4d=2910.4
431.2 is only the first day therefore it doesn't need the variable because the variable represents the number of days. 826.4 even says "each remaining day" referring to what the variable represents.